1 Timothy 3:2 - "Now a bishop must be…married only once"
1 Timothy 4:1, 3 - "Now the Spirit expressly says that in later times some will renounce the faith by paying attention to deceitful spirits and teachings of demons…They forbid marriage"
First I will go through these two passages and explain why they don't go against priestly celibacy, and then I will give biblical support for priestly celibacy.
First, 1 Timothy 3:2. Here, Paul is saying that if a bishop is married, he must have only one wife. This was a time when polygamy was popular among pagans, and Paul was instructing Timothy not to go along with this pagan practice. He is NOT saying that a bishop HAS to be married. Why must a bishop be married? If we interpret the rest of 1 Timothy 3:1-7 this same way, we would conclude that bishops must have children, and they must have more than one (verse 4). Now, Protestants will then say that while this passage does not say that priests must marry, it does approve of priests marrying. The Catholic answer to this is that we agree; there really is nothing wrong with priests marrying, but Church law says that priests cannot marry. Priestly celibacy is not doctrine; it can change. In fact, it was implemented during the Middle Ages. So, what proof against priestly celibacy does this passage give? All it says is that priests marrying is not wrong; it doesn't say that priests HAVE to be able to marry.
Now, 1 Timothy 4:1, 3. Here, Paul is warning against people who forbid ALL marriage. Does the Church forbid ALL marriage? No! Marriage is a SACRAMENT! What proof against priestly celibacy does this passage offer? None whatsoever.
Now for some biblical proofs FOR priestly celibacy.
Matthew 19:12 - "For there are eunuchs who have been so from birth, and there are eunuchs who have been made eunuchs by others, and there are eunuchs who have made themselves eunuchs for the sake of the kingdom of heaven. Let anyone accept this who can."
1 Corinthians 7:7-38 - "I wish that all were as I myself am. But each has a particular gift from God, one having one kind and another a different kind. To the unmarried and the widows I say that it is well for them to remain as I am…Are you free from a wife? Do not seek a wife…The unmarried man is anxious about the affairs of the Lord, how to please the Lord; but the married man is anxious about the affairs of the world, how to please his wife, and his interests are divide."
So, while there's nothing sinful about priests marrying (1 Timothy 3:2), the Church has decided that it is better for priests not to marry because they can focus all their attention on God (Matthew 19:12, 1 Corinthians 7:7-38). Priestly celibacy is NOT doctrine; it is a discipline instituted during the Middle Ages that CAN change. It is not an infallibly proclaimed dogma of the Church; it is not an eternal, unchanging truth like Jesus' divinity. Rather, she just feels that it is better that priests don't marry so they will be able to focus all their time and energy on God.